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# A-level Maths - ln(x) - Natural Logs... HELP?

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1. Ok so last night I had trouble trying to figure out how this makes sense. I can't get my head round why this is...

2. (Original post by Philip-flop)
Ok so last night I had trouble trying to figure out how this makes sense. I can't get my head round why this is...

You should've covered this in C2. It's one of the logarithm rules. Or are you asking for the proof?
3. (Original post by Philip-flop)
Ok so last night I had trouble trying to figure out how this makes sense. I can't get my head round why this is...

It's the rule that .

Let then .

So .

Take the logarithm of both sides .

So
4. (Original post by Philip-flop)
Ok so last night I had trouble trying to figure out how this makes sense. I can't get my head round why this is...

You know
ln(x) + ln(y) =ln(xy)
let y=x
ln(x) +ln (x) = ln(x^2)
2ln(x) = ln(x^2)
You can extend the rule (forwards and backwards) to end up with any rational power and it still works (for irrationals you need Zacken's method)
5. (Original post by RDKGames)
You should've covered this in C2. It's one of the logarithm rules. Or are you asking for the proof?
Oh my god. Yeah of course!! I completely forgot! My Maths brain still hasn't switched on since the summer!

(Original post by Zacken)
It's the rule that .

Let then .

So .

Take the logarithm of both sides .

So
Thank you Zacken!!
Can always rely on you for amazing explanations

(Original post by ValerieKR)
You know
ln(x) + ln(y) =ln(xy)
let y=x
ln(x) +ln (x) = ln(x^2)
2ln(x) = ln(x^2)
You can extend the rule to any power and it still works
Thank you so much!! Can't believe I forgot the "Powers of Logs" rule
6. Hi mate - I'll explain this stuff to you next week if you like ;-)
7. (Original post by Paulxo)
Hi mate - I'll explain this stuff to you next week if you like ;-)
Don't you worry, I have a looooooong list of questions I need to ask you :P
8. (Original post by Philip-flop)
Oh my god. Yeah of course!! I completely forgot! My Maths brain still hasn't switched on since the summer!

Thank you Zacken!!
Can always rely on you for amazing explanations

Thank you so much!! Can't believe I forgot the "Powers of Logs" rule
No worries
9. Ok I seem to be slipping up on Natural Logs again FFS. Why can't I do part a and c?

For part c I end up with
10. (Original post by Philip-flop)
Ok I seem to be slipping up on Natural Logs again FFS. Why can't I do part a and c?

For part c I end up with

Wait, how can you not do A and C when you've done B then...? I'm assuming you've done B since you're not asking for help on it...
11. (Original post by Philip-flop)
For part c I end up with
^.-
12. (Original post by RDKGames)

Wait, how can you not do A and C when you've done B then...? I'm assuming you've done B since you're not asking for help on it...
I think I worked out part b as a fluke
Here's my answer for part b...

Am I rubbish at Logs?
13. (Original post by Philip-flop)
I think I worked out part b as a fluke
Here's my answer for part b...

Am I rubbish at Logs?
It's technically correct but doesn't really flow well towards the end without converting the 4 into a power of 2.
14. (Original post by Philip-flop)
Ok I seem to be slipping up on Natural Logs again FFS. Why can't I do part a and c?

For part c I end up with
You're correct on part c - Remember that aln(x)= ln(x^a) even when a is negative

start part a by taking logs of both sides
15. On b, how did you turn ln 4/2 into ln 2?
16. (Original post by Paulxo)
On b, how did you turn ln 4/2 into ln 2?
Because ? I don't know
17. (Original post by ValerieKR)
You're correct on part c - Remember that aln(x)= ln(x^a) even when a is negative

start part a by taking logs of both sides
Ok I've gone wrong with part a as well

18. Great. I don't know how to even write e^3x in latex. Here is my answer below...

I am aware that I am completely wrong with my answer so try to look past my stupidity and help me if you can
19. (Original post by Philip-flop)
Great. I don't know how to even write e^3x in latex. Here is my answer below...

I am aware that I am completely wrong with my answer so try to look past my stupidity and help me if you can

This is correct. However, if this is Exercise 3B, Question 2A you need to give your answer in terms of .

Don't call yourself stupid just because you can't solve a math problem. Everyone who is assisting you in this thread has been doing maths way longer than you. So, they'll obviously be a little bit sharper at it...
20. (Original post by Naruke)
This is correct. However, if this is Exercise 3B, Question 2A you need to give your answer in terms of .

Don't call yourself stupid just because you can't solve a math problem. Everyone who is assisting you in this thread has been doing maths way longer than you. So, they'll obviously be a little bit sharper at it...
Oh yay. At least I kind of got the question right. But how do I give my answer in terms of ??

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